Let a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0 be the two lines.

(a) The lines intersect if is true.

(b) The lines are parallel if is true.

(c) The lines are coincident if is true.

(i) Given: 2x + y − 1 = 0 and 3x + 2y + 5 = 0

Explanation:

Here,

Therefore, the lines 2x + y − 1 = 0 and 3x + 2y + 5 = 0 intersect.

(ii) Given: x − y = 0 and 3x − 3y + 5 = 0

Explanation:

Here,

Therefore, the lines x − y = 0 and 3x − 3y + 5 = 0 are parallel.

(iii) Given: 3x + 2y − 4 = 0 and 6x + 4y − 8 = 0

Explanation:

Here,

Therefore, the lines 3x + 2y − 4 = 0 and 6x + 4y − 8 = 0 are coincident.